How Is Satellite Orbit Speed Calculated with Atmospheric Resistance?

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Discussion Overview

The discussion centers on how to calculate the orbital speed of a satellite when it is affected by atmospheric resistance, such as drag from a thin atmosphere or solar wind. Participants explore the implications of orbital decay and the relationship between deceleration and changes in orbital speed and height.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes that atmospheric resistance causes a satellite to decelerate, which leads to a decrease in altitude and an increase in orbital speed, raising the question of how to calculate this new speed.
  • Another participant suggests researching "orbital decay" to understand the mechanics involved with drag forces affecting orbits.
  • A third participant mentions a specific resistance value and expresses uncertainty about how to calculate the resulting change in orbital speed.
  • One participant proposes that the change in speed due to drag can be calculated by multiplying the constant deceleration by time, but notes that a more accurate method would involve numerical integration of instantaneous deceleration over time.
  • This participant also emphasizes that the primary interest in orbital decay is often the change in orbital height rather than speed, as low drag tends to circularize the orbit before lowering its overall height.

Areas of Agreement / Disagreement

Participants express various viewpoints on the relationship between drag, speed, and orbital height, indicating that there is no consensus on the best approach to calculate the new orbital speed in the presence of atmospheric resistance.

Contextual Notes

Some assumptions about the constancy of deceleration and the specific conditions under which these calculations apply are not fully explored, leaving room for further clarification and discussion.

Bjarne
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When a satellite is affected by resistance against orbit motion,
for example from thin atmosphere or solar wind, it will as a result of this decelerates -
but in that process it will decrease slightly toward the earth, and therefore following accelerate too.
How can the new orbit speed be calculated?
 
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You may want to search and read up on the concept of "orbital decay" to get an idea of how orbital mechanics works in the presence of drag forces.
 
Filip Larsen said:
You may want to search and read up on the concept of "orbital decay" to get an idea of how orbital mechanics works in the presence of drag forces.

I tried, and found how to calculate a lot related to that question, but now how to calculate orbit speed change.

Let's say the resistance against motion is 1E-10m/s^2
Due to the resistance the satellite will decrease towards the Earth, and hence the orbit speed will also increase, as well as it will decrease due to the resistance.
 
From an assumed constant deceleration due to drag you can find the change in speed due to this deceleration simply by multiplying with time. In a more detailed calculation you would instead (numerically) integrate the instantaneous deceleration over a period of time, along with other accelerations, in order to get a more accurate trajectory of the satellite.

But I'm not sure why you'd want to know this? In general, as long as the change in speed is low enough for the satellite still to be in orbit, then the most significant effect of the drag at any particular point in the orbit is to reduce the orbital height at the opposite side of the orbit. This means that low drag generally acts to first circularize the orbit and then, when the orbit is mostly circular, to lower the overall height. Thus, the change in orbital speed due to drag is closely connected to the change in orbital height, and it is usually the orbital height, rather than speed, that is in primary interest when you look at orbital decay.
 

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